The viscous characteristics of granular fault gouge significantly impact the dynamic mechanical behavior of faults, yet the problem of determining the viscosity of these interlayers at different slip velocities remains unresolved. This article presents theoretical research on this issue. The Maxwell relaxation model was employed to study the evolution of force chains in granular fault gouge during slow shearing of granular gouge, and the dependence of force chain length on shear strain rate, effective extension speed of shear bands, and strength of the granular medium was derived. The relaxation time of the shear band in granular fault gouge, the expression for the viscosity coefficient of the granular medium, and the conditions for the transformation of solid-liquid mechanical behavior of the granular medium were established. The validity of this model was verified through comparison with existing experimental data. For high-speed fault slip shear, the motion of the granular medium exhibits turbulent characteristics. Statistical physics was used to describe the interaction between granular particles in granular fault gouge, and it was found that the viscosity coefficient is inversely proportional to the shear rate at high slip rates. The research results have fundamental significance for understanding the viscous and other physico-mechanical properties of granular gouge in faults.

Experimental studies show that the dynamic size effect is opposite to the static size effect of rock strength, but the intrinsic micro-dynamic mechanism of the dynamic size effect of rocks has not been clarified yet. In this paper, sandstone sample is selected as the research object, and based on the wing-crack model of rock, the crack motion equation and loading equation of sample are jointly calculated, the mechanism of rock specimen size on strength under dynamic loading, namely the dynamic size effect of rock strength is analyzed. The results show that: Under the same dynamic loading rate, with the larger the specimen size, more time is required for crack coalescence, and the applied stress at the moment of the specimen failure (dynamic strength) is greater, the dynamic size effect is more evident, and the rock dynamic strength increases with strain rate approximately in a power law; The critical strain rate range at a definite size range of specimen of rock is obtained by numerical calculation, and the static size effect takes the dominant position when the strain rate is below the critical strain rate, while the dynamic size effect dominates when the strain rate is above the critical strain rate, and the critical strain rate decreases with the increase of specimen size; The critical size of the specimen decreases with the increase of the strain rate.

This study investigates the causes of permeability decline in porous reservoirs under decreasing reservoir pressure by comparing laboratory experiments with well test data. Well tests indicate a greater sensitivity of permeability to pressure changes in reservoir formations compared to laboratory conditions and for this remain unclear. Field studies of permeability changes in northern Perm oil fields were conducted alongside laboratory experiments on core permeability under pressure. Results showed that highly permeable samples exhibited the greatest decline in permeability during elastic deformations, with reductions of 6% for limestones and 20% for sandstones. The relationship between permeability and purely elastic deformations for both rock types was accurately described by a power law. By comparing coefficients from field and lab studies, the mechanism of permeability decline in field conditions was established. A model incorporating elastic and plastic deformations of porous reservoirs was developed. The model considers the localization of plastic deformations in horizontal and vertical low-permeability deformation bands. Findings indicate that highly permeable formations are more susceptible to deformation band formation, particularly in thicker layers. The decrease in permeability was found to correlate strongly with the formation thickness, likely due to the formation of transverse deformation bands in pore layers.